Nonadiabatic Molecular Dynamics with Non-Condon Effect of Charge Carrier Dynamics

Nonradiative multiphonon transitions play a crucial role in understanding charge carrier dynamics. To capture the non-Condon effect in nonadiabatic molecular dynamics (NA-MD), we develop a simple and accurate method to calculate noncrossing and crossing k-point NA coupling in momentum space on an equal footing and implement it with a trajectory surface hopping algorithm. Multiple k-point MD trajectories can provide sufficient nonzero momentum multiphonons coupled to electrons, and the momentum conservation is maintained during nonvertical electron transition. The simulations of indirect bandgap transition in silicon and intra- and intervalley transitions in graphene show that incorporation of the non-Condon effect is needed to correctly depict these types of charge dynamics. In particular, a hidden process is responsible for the delayed nonradiative electron-hole recombination in silicon: the thermal-assisted rapid trapping of an excited electron at the conduction band minimum by a long-lived higher energy state through a nonvertical transition extends charge carrier lifetime, approaching 1 ns, which is about 1.5 times slower than the direct bandgap recombination. For graphene, intervalley scattering takes place within about 225 fs, which can occur only when the intravalley relaxation proceeds to about 50 fs to gain enough phonon momentum. The intra- and intervalley scattering constitute energy relaxation, which completes within sub-500 fs. All the simulated time scales are in excellent agreement with experiments. The study establishes the underlying mechanisms for a long-lived charge carrier in silicon and valley scattering in graphene and underscores the robustness of the non-Condon approximation NA-MD method, which is suitable for rigid, soft, and large defective systems.